How quickly stars streak depends on the focal length you are using. Generally, you can get away with a 30-40 second exposure for wider angles, as the amount of star movement in that time doesn't show too vividly. Add in some telephoto focal lengths though, and movement can start to show up very quickly, even 10 seconds or less.
Star shots will depend on general sky visibility where you are. Where I live, you might see 1-10 stars on any given night. If it's very clear, with no clouds, haze, or fog, and the temperatures are cooler, we might see a few dozen. That's it. We have horrible light pollution, poor atmospheric conditions (humidity, haze, marine layer), sea-level altitude, and are often very cloudy and with some pollution. It takes long exposures here with very high ISO to really have much of a chance to see stars in a photo - either that, or hurricanes (our best star viewing came after a hurricane in 2005 - power was knocked out across the state, so no light pollution - no cars were on the roads which were blocked with trees - no pollution from buildings and cars - no clouds or atmospheric issues as a cold front followed and the hurricane dragged everything out to sea).
I've also lived in the western US, where I was close to the high altitude deserts...out in the desert, away from any nearby city, and with clear skies and cold temps, you could see billions of stars in perfect clarity - you would need nothing more than a P&S camera and could get a photo of them by snapshot.
In general, one of the best methods to avoiding noise while still catching stars as brightly as possible, and also avoiding too much star trail movement, it to use multiple exposures. You can shoot shorter 10 second bursts, ISO1600 for better sensitivity, then stack the multiple exposures to eliminate noise across the frames. The downside is alignment - take 10 photos over a 2-4 minute period, and the stars all will have moved within the frames - you can go through the painstaking alignment of the frames using 'difference' layering, or get a star-tracking type base or pod unit that moves the camera with the stars - with those units, you can also go for much longer exposures, into the minutes, if you want.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses